Question

A circular shaft shown in the figure is subjected to torsion T at two points A & B. The torsional rigidity of portions CA & BD is $G{J}_1$ and that of portion AB is $G{J}_2$. The rotations of shaft at points A and B are ${\theta }_1$&${\theta }_2$. The rotation ${\theta }_1$ is

• A. $\frac{TL}{G{J}_1+G{J}_2}$
• B. $\frac{TL}{G{J}_1}$
• C. $\frac{TL}{G{J}_2}$
• D. $\frac{TL}{G{J}_1-G{J}_2}$

Answer 1

The correct option is B $\frac{TL}{G{J}_1}$



Structure and loading is symmetrical about mid point so torsional moment generated at C and D will be equal to T.



Using Torsion formula,

$\frac{T}{J}=\frac{G\theta }{L}$

${\theta }_1=\frac{TL}{G{J}_1}$